Causation without Correlation is Possible
theincidentaleconomist.com
Causation without Correlation is Possible
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Re: Causation without Correlation is Possible
#2The submitted article links out to a more scholarly article
http://www.springerlink.com/content/l787673gxg8425g6/fulltex...
with diagrams about issues to consider in observational studies.
I always like to recommend Peter Norvig's article on interpreting research studies
http://norvig.com/experiment-design.html
and in the medical context can also recommend Harriet Hall's lecture notes
http://www.skepticstoolbox.org/hall/
as examples of popular writings on research study interpretation that give vivid examples and bring up important issues.
Re: Causation without Correlation is Possible
#3No statistical method can prove causality. Also, there's no scientific method to confirm any one of causal relationships, either. Causality exists only in human mind. There's no methodic way to discern semipermanent coincidence (or identical equivalence) from causality.
Re: Causation without Correlation is Possible
#4>Causation without correlation. ...Suppose the value of y is known to be caused by x. The true relationship between x and y is mediated by another factor, call it A, that takes values of +1 or -1 with equal probability. The true process relating x to y is y = Ax.
>It is a simple matter to show that the correlation between x and y is zero. Perhaps the most intuitive way is to imagine many samples (observations) of x, y pairs. Over the sub-sample for which the pairs have the same sign (i.e. for which A happened to be +1) y=x and the correlation is 1. Over the sub-sample for which the pairs have the opposite signs (i.e. for which A happened to be -1) y=-x and the correlation is -1. Since A is +1 and -1 with equal probability, the contributions to the total correlation from the two sub-samples cancel, giving a total correlation of zero.
It seems to me that this doesn't quite make sense. Sure, the correlation of the average of the numbers is 0, but notice that |x - y| <= |2x|, or that |y| = |x|. That seems like a rather large correlation to me, even though half the time, x and y are positively correlated, and the other half, they're negatively correlated.
Re: Causation without Correlation is Possible
#5It would be wonderful if the first line were true.
"It is well known that correlation does not prove causation."
Causality itself is hypothetical, an artifact of perception.
Re: Causation without Correlation is Possible
#6Long story short: causation without correlation is possible if you are unable to adjust for confounding.
Re: Causation without Correlation is Possible
#7>Causation without correlation. ...Suppose the value of y is known to be caused by x. The true relationship between x and y is mediated by another factor, call it A, that takes values of +1 or -1 with equal probability. The true process relating x to y is y = Ax. >It is a simple matter to show that the correlation between x and y is zero. Perhaps the most intuitive way is to imagine many samples (observations) of x,…
A paragraph or so down, he says "That is, there are functions of x and functions of y that are correlated." So, for your example, could we consider Abs value as a function?
Re: Causation without Correlation is Possible
#8>Causation without correlation. ...Suppose the value of y is known to be caused by x. The true relationship between x and y is mediated by another factor, call it A, that takes values of +1 or -1 with equal probability. The true process relating x to y is y = Ax. >It is a simple matter to show that the correlation between x and y is zero. Perhaps the most intuitive way is to imagine many samples (observations) of x,…
Yes, you would certainly notice this as you plotted the points.
Re: Causation without Correlation is Possible
#9>Causation without correlation. ...Suppose the value of y is known to be caused by x. The true relationship between x and y is mediated by another factor, call it A, that takes values of +1 or -1 with equal probability. The true process relating x to y is y = Ax. >It is a simple matter to show that the correlation between x and y is zero. Perhaps the most intuitive way is to imagine many samples (observations) of x,…
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Re: Causation without Correlation is Possible
#10It would be wonderful if the first line were true. "It is well known that correlation does not prove causation." Causality itself is hypothetical, an artifact of perception.
That's the subject of the next post on this topic, forthcoming.